(8,21+9,73)-0,001=
<em>Сначала</em><em> </em><em>выполняем</em><em> </em><em>действие</em><em> </em><em>в</em><em> </em><em>скобках</em><em>(</em><em>сложение</em><em>)</em><em>=</em><em>8,21</em><em>+</em><em>9,73</em><em>=</em><em>17,94</em>
<em>Затем</em><em> </em><em>выполняем</em><em> </em><em>вычитание</em><em>=</em><em>17,94-0,001</em><em>=</em><em>17,939</em>
4,08*28,6 - 18,6*4,08=40,8
Ответ:
8000
2000
Объяснение:
вроде бы так, но я не уверенна
Пользуясь определением , найдите производную функции f(x) в точке x0
f(x)=1-4x,x0=3
Решение:
Используя определение производной, имеем
![f'(x_0)=\displaystyle \lim_{зx\to0}\frac{f(x_0+зx)-f(x_0)}{зx}=\lim_{зx\to0}\frac{1-4(x_0+зx)-1+4x_0}{зx}=\\ \\ \lim_{зx\to0}\frac{1-4x_0-4зx-1+4x_0}{зx}=-\lim_{зx\to0}\frac{4зx}{зx}=-4](https://tex.z-dn.net/?f=f%27%28x_0%29%3D%5Cdisplaystyle+%5Clim_%7B%D0%B7x%5Cto0%7D%5Cfrac%7Bf%28x_0%2B%D0%B7x%29-f%28x_0%29%7D%7B%D0%B7x%7D%3D%5Clim_%7B%D0%B7x%5Cto0%7D%5Cfrac%7B1-4%28x_0%2B%D0%B7x%29-1%2B4x_0%7D%7B%D0%B7x%7D%3D%5C%5C+%5C%5C+%5Clim_%7B%D0%B7x%5Cto0%7D%5Cfrac%7B1-4x_0-4%D0%B7x-1%2B4x_0%7D%7B%D0%B7x%7D%3D-%5Clim_%7B%D0%B7x%5Cto0%7D%5Cfrac%7B4%D0%B7x%7D%7B%D0%B7x%7D%3D-4)
найдите производную функции
f(x)=(x^2+5)(x^3-2x+2)
f(x)= (x^2-3x)/(1-2x)
f(x)=(3-2x^3)^5
Решение:
![f'(x)=(x^2+5)'(x^3-2x+2)+(x^2+5)(x^3-2x+2)'=\\ =2x(x^3-2x+2)+(x^2+5)(3x^2-2)=2x^4-4x^2+4x+3x^4+13x^2-10=\\ =5x^4+9x^2+4x-10](https://tex.z-dn.net/?f=f%27%28x%29%3D%28x%5E2%2B5%29%27%28x%5E3-2x%2B2%29%2B%28x%5E2%2B5%29%28x%5E3-2x%2B2%29%27%3D%5C%5C+%3D2x%28x%5E3-2x%2B2%29%2B%28x%5E2%2B5%29%283x%5E2-2%29%3D2x%5E4-4x%5E2%2B4x%2B3x%5E4%2B13x%5E2-10%3D%5C%5C+%3D5x%5E4%2B9x%5E2%2B4x-10)
![f'(x)=\dfrac{(x^2-3x)'(1-2x)-(x^2-3x)(1-2x)'}{(1-2x)^2}=\\ \\ =\dfrac{(2x-3)(1-2x)+2(x^2-3x)}{(1-2x)^2}=\dfrac{-4x^2+8x-3+2x^2-6x}{(1-2x)^2}=\\ \\ =\dfrac{-2x^2+2x-3}{(1-2x)^2}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cdfrac%7B%28x%5E2-3x%29%27%281-2x%29-%28x%5E2-3x%29%281-2x%29%27%7D%7B%281-2x%29%5E2%7D%3D%5C%5C+%5C%5C+%3D%5Cdfrac%7B%282x-3%29%281-2x%29%2B2%28x%5E2-3x%29%7D%7B%281-2x%29%5E2%7D%3D%5Cdfrac%7B-4x%5E2%2B8x-3%2B2x%5E2-6x%7D%7B%281-2x%29%5E2%7D%3D%5C%5C+%5C%5C+%3D%5Cdfrac%7B-2x%5E2%2B2x-3%7D%7B%281-2x%29%5E2%7D)
![f'(x)=((3-2x^3)^5)'=5(3-2x^3)^4\cdot(3-2x^3)'=-30x^2(3-2x^3)^4](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%283-2x%5E3%29%5E5%29%27%3D5%283-2x%5E3%29%5E4%5Ccdot%283-2x%5E3%29%27%3D-30x%5E2%283-2x%5E3%29%5E4)